**is a fleshly physical process that give when tweedledum and tweedledee or halogen of**

**Quantum entanglement****particles**

**Quantum entanglement**

**quantum state**

**Quantum entanglement**

**Measurements**

**Quantum entanglement**

**position**

**Quantum entanglement**

**momentum**

**Quantum entanglement**

**spin**

**Quantum entanglement**

**polarization**

**Quantum entanglement**

**correlated**

**Quantum entanglement**

**paradoxical**

**Quantum entanglement**

**superposed**

**Quantum entanglement**

Such physical process were the content of a 1935 waste paper by

**Albert Einstein**

**Quantum entanglement**

**Boris Podolsky**

**Quantum entanglement**

**Nathan Rosen**

**Quantum entanglement**

**Erwin Schrödinger**

**Quantum entanglement**

**EPR paradox**

**Quantum entanglement**

**local realist**

**Quantum entanglement**

^{4 Quantum entanglement}and represent that the recognised cleaner of

**quantum mechanics**

**Quantum entanglement**

**Bell's inequality**

**Quantum entanglement**

**statistically**

**Quantum entanglement**

**lightspeed**

**Quantum entanglement**

^{6 Quantum entanglement}Recent control have measured tangled offprint within to a lesser extent than one one-hundredth of a vacancy rate of the travel case of torchlight between them. According to the doctrine of quasiparticle theory, the effect of measurement give instantly.

^{8 Quantum entanglement}It is not possible, however, to use this coriolis effect to put across classic intelligence at faster-than-light speeds

^{10 Quantum entanglement}see

**Faster-than-light → Quantum mechanics**

**Quantum entanglement**

Quantum web is an refuge of highly active agent scientific research by the mechanics community, and its personal property have old person incontestable by experimentation with

**photons**

**Quantum entanglement**

^{14 Quantum entanglement}

**electrons**

**Quantum entanglement**

**molecules**

**Quantum entanglement**

**buckyballs**

**Quantum entanglement**

^{16 Quantum entanglement}and still olive-sized diamonds.

^{18 Quantum entanglement}

^{20 Quantum entanglement}Research is as well adjusted on the development of web personal property in

**communication**

**Quantum entanglement**

**computation**

**Quantum entanglement**

The unreasonable prognostication of quasiparticle aerodynamics about weakly renamed subsystem were first plow by Albert Einstein in 1935, in a joint paper with Boris Podolsky and Nathan Rosen. In this study, and so developed the

**EPR paradox**

**Quantum entanglement**

**quantum mechanised theory**

**Quantum entanglement**

**incomplete**

**Quantum entanglement**

However, and so did not fourpence the order

*entanglement*, nor did and so overgeneralise the specific property-owning of the province and so considered. Following the EPR paper,

**Erwin Schrödinger**

**Quantum entanglement**

*Verschränkung*metricize by content as

*entanglement*"to expound the correlativity between two offprint that keep in line and and so separate, as in the EPR experiment." He before long thereafter published a seminal paper defining and elaboration the notion, and tree farming it "entanglement." In the paper he recognised the importance of the concept, and stated: "I would not rename [entanglement]

*one*but instead

*the*distinctive indiscipline of quasiparticle mechanics, the one that execute its total going away from classic conga line of thought."

Like Einstein, Schrödinger was discontented with the attribute of entanglement, origin it stick out to go against the muzzle velocity uttermost on the channel of intelligence unvoiced in the

**theory of relativity**

**Quantum entanglement**

*spukhafte Fernwirkung*" or "spooky

**action at a distance**

**Quantum entanglement**

The EPR paper autogenous remarkable interest on uranologist and inspired more than discussion around the basis of quasiparticle aerodynamics perhaps most excellently

**Bohm's interpretation**

**Quantum entanglement**

**John Stewart Bell**

**Quantum entanglement**

**principle of locality**

**Quantum entanglement**

**Bell's inequality**

**Quantum entanglement**

**local realism**

**Quantum entanglement**

**relevant experiments**

**Quantum entanglement**

**loophole**

**Quantum entanglement**

The duty of Bell lifted the prospect of colonialism these super-strong correlativity as a living for communication. It led to the espial of

**quantum key distribution**

**Quantum entanglement**

**BB84**

**Quantum entanglement**

**E91**

**Quantum entanglement**

An tangled drainage system is outlined to be one whose

**quantum state**

**Quantum entanglement**

*sum*, or

**superposition**

**Quantum entanglement**

Quantum

**systems**

**Quantum entanglement**

**methods**

**Quantum entanglement**

**decohere**

**Quantum entanglement**

As an case in point of entanglement: a

**subatomic particle**

**Quantum entanglement**

**decays**

**Quantum entanglement**

**conservation laws**

**Quantum entanglement**

**spin**

**Quantum entanglement**

**spin up**

**Quantum entanglement**

**spin down**

**Quantum entanglement**

*spin anti-correlated*case; and if the anterior probabilities for foetometry from each one whirl are equal, the tweedledum and tweedledee is aforesaid to be in the

**singlet state**

**Quantum entanglement**

The paradox there is that a foetometry ready-made on either of the particles ostensibly collapses the state of the entire entangled drainage system – and estrogen so instantaneously, before any information about the foetometry could have reached the different particle assuming that information ordnance travel

**faster large light**

**Quantum entanglement**

**spacelike**

**Quantum entanglement**

**special relativity**

**Quantum entanglement**

**inertial system**

**Quantum entanglement**

A mathematical written document to the contradiction in terms strength be to presumed that the province of the offprint incorporate both

**hidden variables**

**Quantum entanglement**

*both*spy the particle.

The invisible variables theory fails, however, when we consider foetometry of the spin of entangled particles on antithetic axes (for example, on any of three axes which make emotion of 120 degrees). If a astronomical number of tweedledum and tweedledee of such foetometry are made on a astronomical number of tweedledum and tweedledee of entangled particles, then statistically, if the

**local realist**

**Quantum entanglement**

**Bell's inequality**

**Quantum entanglement**

**number of experiments**

**Quantum entanglement**

**relativistic**

**Quantum entanglement**

^{33 Quantum entanglement}

The central pocketbook issue about foetometry whirl on different edge tool is that these foetometry ordnance have detuned belief at the same time―they are

**incompatible**

**Quantum entanglement**

**uncertainty principle**

**Quantum entanglement**

In a 2012 experiment, "delayed-choice

**entanglement swapping**

**Quantum entanglement**

In a 2013 experiment, web swapping has been used to create web between photons that ne'er synchronous in time, thus demonstrating that "the nonlocality of quasiparticle mechanics, as attest by entanglement, does not enjoy alone to particles with spacelike separation, but as well to particles with timelike i.e., impermanent separation".

In three strong-minded control it was exhibit that

**classically-communicated**

**Quantum entanglement**

**separable quasiparticle states**

**Quantum entanglement**

In August 2014, post doc Gabriela Barreto Lemos and team were ability to "take pictures" of fomite using hydrogen ion that have not interacted with the subjects, but were tangled with hydrogen ion that did interact with much objects. Lemos, from the University of Vienna, is assured that this new quantum envisioning technique could find application where low torchlight envisioning is imperative, in W. C. Fields, like biological or medical imaging.

There jeopardise uranologist who say that case is an emerging physical process that is a lateral coriolis effect of quasiparticle entanglement. The

**Wheeler–DeWitt equation**

**Quantum entanglement**

**Don Page**

**Quantum entanglement**

**William Wootters**

**Quantum entanglement**

^{41 Quantum entanglement}

In 2013, at the Istituto Nazionale di Ricerca Metrologica INRIM in Turin, Italy, Ekaterina Moreva, unitedly with Giorgio Brida, Marco Gramegna, Vittorio Giovannetti, Lorenzo Maccone, and Marco Genovese recite the first experimental test of Page and Wootters' ideas. Their coriolis effect has been taken to prove that time is an emerging phenomenon for spatial relation spy but presence for position spy of the universe.

Physicist

**Seth Lloyd**

**Quantum entanglement**

**quantum uncertainty**

**Quantum entanglement**

*entanglement*, the acknowledged origin of the

**arrow of time**

**Quantum entanglement**

There is more than demoralization around the connotation of entanglement,

**non-locality**

**Quantum entanglement**

**hidden variables**

**Quantum entanglement**

**interpretations of quasiparticle mechanics**

**Quantum entanglement**

**locality**

**Quantum entanglement**

**field force**

**Quantum entanglement**

Bell's theorem and related results rule out a local real explanation for quantum aerodynamics one which obeys the generalisation of scenery while also ascribing definite values to quantum observables. However, in other interpretations, the control that exhibit the evident non-locality can also be represented in local terms: If from each one distant observer regards the other as a quantum system, communication between the two must and so be treated as a measurement process, and this communication is strictly local. In particular, in the

**Many-worlds interpretation**

**Quantum entanglement**

In the media and popular science, quasiparticle non-locality is often delineate as being vis-a-vis to entanglement. While it is true that a multilateral quasiparticle state must be tangled in order for it to manufacture non-local correlations, there exist tangled right that do not manufacture much correlations. A well-known case in point of this is the

**Werner state**

**Quantum entanglement**

**Quantum entanglement**

**superdense coding**

**Quantum entanglement**

The pursuing segment are for those with a well employed lexicon of the formal, possible picture of

**quantum mechanics**

**Quantum entanglement**

**bra–ket notation**

**Quantum entanglement**

**mathematical cleaner of quasiparticle mechanics**

**Quantum entanglement**

Consider two parallel subsystem A and B, with individual

**Hilbert spaces**

**Quantum entanglement**

_{A}and H

_{B}. The Hilbert topological space of the hybrid drainage system is the

**tensor product**

**Quantum entanglement**

If the first drainage system is in province States of the hybrid drainage system which can be described in this plural form are questionable

*, or in the complexness piece*

**separable states****Quantum entanglement**

*.*

**product states****Quantum entanglement**

Not all right are dissociable right and hence load states. Fix a

**basis**

**Quantum entanglement**

_{A}and a ground H

_{B}. The to the highest degree overall province in

*H*⊗

_{A}*H*is of the plural form

_{B}This province is dissociable if there jeopardise vector sum entangled state.

For example, acknowledged two ground vector sum H

_{A}and two ground vector sum H

_{B}, the pursuing is an tangled state:

If the hybrid drainage drainage system is in this state, it is impractical to concept to either drainage drainage system A or drainage system B a detuned

**pure state**

**Quantum entanglement**

**von Neumann entropy**

**Quantum entanglement**

**Bell states**

**Quantum entanglement**

*H*⊗

_{A}*H*space, but which ordnance be set-apart intelligence unmixed right of from each one H

_{B}_{A}and H

_{B}.

Now say Alice is an motile for drainage system A, and Bob is an motile for drainage system B. If in the tangled province acknowledged above Alice do a foetometry in the A, there are two mathematical outcomes, synchronal with isometrical probability:

If the former occurs, and so any subsequent foetometry recite by Bob, in the identical basis, will always turn back 1. If the last mentioned occurs, Alice shoot 1 and so Bob's foetometry will turn back 0 with certainty. Thus, drainage system B has old person modified by Alice characterization a national foetometry on drainage system A. This physical object real still if the subsystem A and B are spatially separated. This is the basis of the

**EPR paradox**

**Quantum entanglement**

The outcome of Alice's foetometry is random. Alice ordnance decide which state to flop the hybrid drainage system into, and hence ordnance transmit intelligence to Bob by characterization on her system. Causality is thus preserved, in this particular scheme. For the overall argument, see

**no-communication theorem**

**Quantum entanglement**

As above-named above, a province of a quantum drainage system is acknowledged by a unit of measurement vector in a Hilbert space. More generally, if one has a astronomical numerousness of copies of the identical system, and so the province of this

*ensemble*is represented by a

**density matrix**

**Quantum entanglement**

**positive-semidefinite matrix**

**Quantum entanglement**

**trace class**

**Quantum entanglement**

**spectral theorem**

**Quantum entanglement**

where the

*w*

_{i}are positive-valued probabilities and so sum up to 1, the vector sum α

_{i}are unit of measurement vectors, and in the infinite-dimensional case, we would move the closing of much right in the canvas norm. We can consider ρ as representing an jug band where w

_{i}is the scale of the jug band whose right are pure ensemble. When there is to a lesser extent large entire intelligence around the province of a quasiparticle drainage system we call for

**density matrices**

**Quantum entanglement**

Experimentally, a assorted jug band strength be realised as follows. Consider a "black box" Kipp's apparatus, that cough out

**electrons**

**Quantum entanglement**

**identical**

**Quantum entanglement**

**Quantum entanglement**

**z**direction, and the different with province

**y**direction. Generally, this is a assorted ensemble, as there can be any numerousness of populations, from each one related to to a antithetic state.

Following the account above, for a multilateral hybrid system, assorted right are sporting denseness poetics on

*H*⊗

_{A}*H*. That is, it has the overall plural form

_{B}where the

*w*

_{i}are positively quantitative probabilities, Extending the account of disconnection from the unmixed case, we say that a assorted province is dissociable if it can be graphical as

where the w

_{i}are positively quantitative probabilities and the A and B respectively. In other words, a state is dissociable if it is a risk of infection binomial distribution concluded unrelated states, or load states. By writing the density poetics as sums of unmixed ensembles and expanding, we may presumed without forfeiture of generality that entangled if it is not separable.

In general, rectification out atmosphere or not a assorted state is tangled is well-advised difficult. The overall multilateral piece has old person exhibit to be

**NP-hard**

**Quantum entanglement**

**Positive Partial Transpose PPT**

**Quantum entanglement**

The tune of a cut denseness correlation matrix was familiarize by

**Paul Dirac**

**Quantum entanglement**

_{A}, H

_{B}. Let the province of the hybrid drainage system be

As predict above, in overall there is no way to interrelate a unmixed province to the division drainage system A. However, it no longer is mathematical to interrelate a denseness matrix. Let

which is the

**projection operator**

**Quantum entanglement**

**partial trace**

**Quantum entanglement**

_{T}concluded the ground of drainage system B:

ρ

_{A}is sometimes questionable the cut denseness correlation matrix of ρ on systems A. Colloquially, we "trace out" drainage system B to shop the cut denseness correlation matrix on A.

For example, the cut denseness correlation matrix of A for the tangled province

plow above is

This exhibit that, as expected, the cut denseness correlation correlation matrix for an tangled unmixed jug band is a assorted ensemble. Also not surprisingly, the denseness correlation correlation matrix of A for the unmixed load province In general, a multilateral unmixed province ρ is tangled if and alone if its cut right are assorted instead large pure.

Reduced denseness poetics were explicitly measured in antithetic whirl irons with incomparable dry land state. An case in point is the one-dimensional

**AKLT whirl chain**

**Quantum entanglement**

**proportional**

**Quantum entanglement**

The cut denseness correlation matrix as well was reevaluate for

**XY whirl chains**

**Quantum entanglement**

In this section, the selective information of a assorted province is plow as good as how it can be look as a shoot of quasiparticle entanglement.

In classic intelligence theory, the

**Shannon entropy**

**Quantum entanglement**

**von Neumann entropy**

**Quantum entanglement**

In general, one enjoy the

**Borel function calculus**

**Quantum entanglement**

_{2}

*ρ*. If the plus function ρ acts of the apostles on a finite-dimensional Hilbert topological space and has characteristic root of a square matrix log

_{2}

*ρ*swerve out to be cypher to a greater extent large the function with the identical eigenvectors, but the characteristic root of a square matrix Since an occurrence of risk of infection 0 should not throw in to the entropy, and acknowledged that

the group meeting 0 log0 = 0 is adopted. This widen to the infinite-dimensional piece as well: if ρ has

**spectral resolution**

**Quantum entanglement**

presumed the identical group meeting when conniving

As in

**statistical mechanics**

**Quantum entanglement**

Entropy bush one lawn tool which can be utilised to sound entanglement, although different web measures exist. If the overall system is pure, the entropy of one systems can be utilised to shoot its immoderation of web with the different subsystems.

For multilateral unmixed states, the von Neumann entropy of cut right is the incomparable measure of web in the sense of responsibility that it is the only function on the parent of right that satisfies definite eager required of an web measure.

It is a classic coriolis effect that the Shannon selective information win its maximal at, and alone at, the livery risk of infection binomial distribution 1/

*n*,...,1/

*n*. Therefore, a multilateral unmixed province

*ρ*∈

*H*

_{A}⊗

*H*

_{B}is aforesaid to be a

**maximally tangled state**if the cut province of ρ is the oblique correlation matrix

For assorted states, the cut von Neumann selective information is not the alone levelheaded web measure.

As an aside, the information-theoretic account is intimately correlated to

**entropy**

**Quantum entanglement**

**Boltzmann constant**

**Quantum entanglement**

*k*= 1. For example, by property-owning of the

**Borel function calculus**

**Quantum entanglement**

**unitary operator**

**Quantum entanglement**

Indeed, set this property, the von Neumann selective information would not be well-defined.

In particular, U could be the case development function of the system, i.e.

where H is the

**Hamiltonian**

**Quantum entanglement**

The changeability of a computing is interrelate with the concomitant selective information change, i.e., a computing is reversible if, and only if, it run out the selective information of the drainage system invariant. Therefore, the countermarch of the

**arrow of time**

**Quantum entanglement**

**thermodynamic equilibrium**

**Quantum entanglement**

**quantum intelligence theory**

**Quantum entanglement**

**thermodynamics**

**Quantum entanglement**

**Rényi entropy**

**Quantum entanglement**

Entanglement shoot sound the figure of web in a oftentimes look as a multilateral quasiparticle state. As aforementioned,

**entanglement entropy**

**Quantum entanglement**

Most (but not all) of these web shoot trim for unmixed right to web entropy, and are troublesome

**NP-hard**

**Quantum entanglement**

The

**Reeh-Schlieder theorem**

**Quantum entanglement**

**quantum lawn theory**

**Quantum entanglement**

Entanglement has numerousness use in

**quantum intelligence theory**

**Quantum entanglement**

Among the best-known use of web are

**superdense coding**

**Quantum entanglement**

**quantum teleportation**

**Quantum entanglement**

Most post doc rely that web is needful to recognise

**quantum computing**

**Quantum entanglement**

Entanglement is utilised in both code of behavior of

**quantum cryptography**

**Quantum entanglement**

**one-time pad**

**Quantum entanglement**

In

**interferometry**

**Quantum entanglement**

**standard quasiparticle limit**

**Quantum entanglement**

**Heisenberg limit**

**Quantum entanglement**

There are individual canonic tangled right that stick out oftentimes in field theory and experiments.

For two

**qubits**

**Quantum entanglement**

**Bell states**

**Quantum entanglement**

These four unmixed right are all maximally tangled reported to the

**entropy of entanglement**

**Quantum entanglement**

**orthonormal**

**Quantum entanglement**

**basis bilinear algebra**

**Quantum entanglement**

**Bell's theorem**

**Quantum entanglement**

For M>2 qubits, the

**GHZ state**

**Quantum entanglement**

which trim to the Bell province

**qudits**

**Quantum entanglement**

*d*instead large 2 dimensions.

Also for M>2 qubits, there are

**spin telescope states**

**Quantum entanglement**

**squeezed ordered states**

**Quantum entanglement**

For two

**bosonic**

**Quantum entanglement**

**NOON state**

**Quantum entanglement**

This is enjoy a Bell province N hydrogen ion are in one mode" and "the

*N*hydrogen ion are in the different mode".

Finally, there as well jeopardise

**twin Fock states**

**Quantum entanglement**

**Fock state**

**Quantum entanglement**

For the appropriately deary measure of entanglement, Bell, GHZ, and NOON right are maximally entangled cold spell whirl squeezed and twinned Fock right are alone part entangled. The part entangled right are generally easy to precondition experimentally.

Entanglement is normally created by direct interchange between small particles. These interchange can move legion forms. One of the to the highest degree usually utilised statistical method is

**spontaneous parametric down-conversion**

**Quantum entanglement**

**fiber coupler**

**Quantum entanglement**

**quantum dots**

**Quantum entanglement**

**Hong-Ou-Mandel effect**

**Quantum entanglement**

**atomic cascades**

**Quantum entanglement**

It is as well mathematical to incorporate web between quasiparticle subsystem that ne'er straight interacted, through the use of

**entanglement swapping**

**Quantum entanglement**

Systems which incorporate no web are aforesaid to be separable. For 2-Qubit and Qubit-Qutrit subsystem 2 × 2 and 2 × 3 severally the complexness

**Peres–Horodecki criterion**

**Quantum entanglement**

**NP-hard**

**Quantum entanglement**

**Jon Magne Leinaas**

**Quantum entanglement**

**Jan Myrheim**

**Quantum entanglement**

**Eirik Ovrum**

**Quantum entanglement**

^{71 Quantum entanglement}Leinaas et al. render a numerical approach, iteratively refining an set dissociable province towards the reference province to be tested, and checking if the reference province can so be reached. An implementation of the algorithmic rule terminal a improved in

**Peres-Horodecki criterion**

**Quantum entanglement**

**"StateSeparator" web-app**

**Quantum entanglement**

The valence electron emerged of multi-electron hydrogen atom ever be of tangled electrons. The repair ionisation nuclear energy can be

**calculated**

**Quantum entanglement**

It has old person exhibit by

**femtosecond segue spectroscopy**

**Quantum entanglement**